Summary

Hercule Poirot, Dr. Constantine, and M. Bouc silently mull over the evidence. At last Poirot sits upright, puffs out his chest, and speaks as if he were "addressing a public meeting." He reveals he has come up with a "certain explanation that would cover the facts as we know them," but it is still somewhat vague and uncertain. To confirm it, he needs to conduct experiments. He then describes how he reached this explanation. Bouc had commented during their first lunch about how the passengers in the first- and second-class coach were of all classes, ages, and nationalities. The coach is full, which is unusual during the winter, and the other coaches are nearly empty. He then details a battery of points, such as the position of the toiletries bag, the charred note, Princess Dragomiroff's "Christian" or first name, and the grease spot on the countess's passport.

Poirot connects the grease spot to the dropped handkerchief, which is monogrammed with the letter H. The only women with a name starting with H are unlikely to own such an expensive handkerchief, but Poirot speculates it is possible an additional woman—the countess—has an initial H in her name and concealed it. The grease stain may have smeared the H in Helena so her name appears as Elena. That this was done intentionally is supported by the wet luggage label on the countess's suitcase. It, too, may have been doctored to conceal the H in her name.

He next explains how the murderer most likely intended the murder to be discovered when the train crossed the Italian border. This plan was derailed by the snowstorm. In fact the train most likely got stranded in the snowbank while the murderer was in Samuel Ratchett's compartment. The murderer stayed in the compartment longer than intended while waiting for the train to start up again, but it never did. Poirot also thinks "the murder was planned to look like an outside job," with the murderer getting off the train at Brod so no suspicion would fall on the passengers. When the train got stuck in the snowbank, the murderer had to improvise and planted clues in an attempt to mislead the investigation.

The threatening letters were, Poirot says, sent to Ratchett primarily to provide evidence of a threat when the police later investigated his murder. But one letter—the one mentioning Daisy Armstrong—was real. It was sent to Ratchett so he would know why he was going to be murdered. The murderer burned the letter after the crime, as it was not intended to be found by the police. The murderer made a mistake, though, and did not burn it fully. This letter indicates someone very closely associated with the Armstrongs is on the train.

The other significant tangible clue is the handkerchief. So far they have been considering this clue from the view it was "dropped unwittingly" by a person "whose initial is H." Poirot suggests an alternative: It may not have been accidentally dropped. Rather, it may have been planted in the dead man's compartment to cast suspicion on someone else. That suspicion would fall on someone closely associated with the Armstrong family, who happens to have a name starting with H. The police would believe they had the correct criminal, as they would have a person with a strong motive and "an incriminating article of evidence." Fearing implication, an innocent person, such as Countess Andrenyi, would then take steps to conceal her Christian name. Thus Poirot concludes the grease-stained passport and wet luggage label do not prove the countess's guilt. They only prove she is anxious to conceal her name.

Bouc questions what connection the countess can have to the Armstrongs, as she says she has never been in America. Poirot responds, "Exactly" and mentions her broken English and exaggerated foreign appearance. He then discusses how Linda Arden, a talented actress, was the grandmother of the Armstrong baby. Her real name was not Arden, however. Instead he thinks it may have been Goldenberg—the same name appearing on the countess's passport. He suggests the countess's real identity is Helena Goldenberg. This would make her Linda Arden's younger daughter and the aunt of the murdered Armstrong baby. She herself is not Hungarian, and she married Count Andrenyi when he was an attaché in Washington, D.C.

Princess Dragomiroff is in on the deception. She recognized the countess as her good friend's younger daughter but did not admit to it to protect her. Likewise, she was intentionally vague about her and lied when she claimed she had married an Englishman in an attempt to deflect suspicion.

Analysis

Poirot's ego and vanity are on full display when he preens before his audience of M. Bouc and Dr. Constantine. Even though he asks them to think, he doesn't expect either to solve the crime. He knows his detecting skills are superior to theirs, and he wants to demonstrate them.

Poirot uses deductive reasoning in his attempts to solve the crime, moving from the general to the specific. For example, Poirot forms a general theory, such as the murderer is someone with a close association with the Armstrong family, and then looks for a specific person with this association. In contrast, Constantine and Bouc use inductive reasoning, which moves from the specific to the general. In other chapters they have identified specific possible suspects and then looked for clues to confirm their suspicions. Christie shows Poirot's approach is the better one. He waits until the facts fit together rather than trying to make the facts fit a theory.

Poirot makes several connections between clues and draws new inferences from them. The first connection is M. Bouc's comment about the diversity of the people on the coach causing him to think how unusual it is for the coach to be full in winter. Two other coaches are nearly empty. This gives a prescient clue essential to solving the murder. Why is one coach full and the others empty? Is it possible all the passengers on this coach are somehow involved in this murder and booked passage on this specific coach for a specific purpose? The latter is likely what Poirot is considering and explains his cryptic comment when he first speaks after thinking—he has thought of something that would explain everything. Rather than explain by providing the possible solution to his two companions, he is going to walk them through the clues and conduct tests to see if his explanation holds up.

Poirot also connects the handkerchief with the smeared passport. He extrapolates from this connection to deduce the handkerchief clue was staged and the passport is not evidence of guilt, as it may seem to be. This causes him to extrapolate further and deduce the crime did not go as planned and other clues were also staged. It also leads him to a new clue, the countess's true identity. If confirmed, it is a major clue to unraveling the crime. The odds of two people related to Daisy Armstrong being on the same coach are too high for coincidence. Poirot is on track, looking at both the big picture and the individual details and using his logic and reasoning skills to see beyond the surface.